It is within the "normal" weight range for your height, which is 114 to 150 pounds.

However, weight does not tell the whole story -- two people of the same height and weight could have greatly different amount of muscle and fat (one may be lean and heavy with muscle, while the other may be flabby). Body fat percentage is more relevant. A simple guide to consider is to measure your waistline at navel level; it should be less than half your height for good health (assuming you are not a pregnant woman).

A 28-inch waist is pretty trim, so it sounds like your weight is within the healthy range. 120 pounds might not necessarily be a reasonable goal for you, especially if you are very active. Active=strong=muscle=mass.

If you are approaching your weight loss goals, but can't quite get there, it might be worth spending a little money to go over your routine in person with a personal trainer and/or a dietician. While regular sessions get expensive, just one or two meetings can teach you a lot. Seeing you in person, they can also likely provide better feedback on whether your goals are reasonable.

I haven't seen you, so I can't say for sure, but you sound like you're in fine shape.

If you were carrying the weight around your waist, that could potentially be a bad thing, but that doesn't appear to be the case, since your waist is slim. For females, it's actually considered healthy to carry weight around the hips and thighs.

A simple guide to consider is to measure your waistline at navel level; it should be less than half your height for good health (assuming you are not a pregnant woman).

Good advice. I would just add, for the sake of accuracy, that one should have their stomach muscles totally relaxed while measuring. If not relaxed, the difference (based on measuring my own waistline) could be as much as 4 1/2 inches. Being totally relaxed while measuring is advice from Dr. Sears of the Zone regimen.

I wouldn't say "chubby" nor "fat".
It might be a few pounds above your optimal weight, but that would depend on your bone structure.
I've known short, small-boned women who were "chubby" at 125 pounds.
And also tall, large-boned women who were quite fit and slim at 150 pounds.

It really all depends on your bone structure, but regardless, if it's overweight at all, it's only a few pounds overweight.